Question

Which of the following could represent the unit side lengths of a right triangle

Answer 1

Answer:

Answer: D 12,16,20

Step-by-step explanation:

The Pythagora's Theorem

On a right triangle with side lengths of a,b, and c, being c the hypotenuse, of the longest side, it follows that:

$a^2+b^2=c^2$

The set {a,b,c} is often called a Pythagorean Triple.

Testing every option:

A

$5^2+8^2=10^2$

$25+64 = 100$

89 = 100

Since equality is false, 5,8,10 are not the side lengths of a right triangle.

B

$3^2+5^2=7^2$

$9+25 = 49$

34 = 49

Since equality is false, 3,5,7 are not the side lengths of a right triangle.

C

$6^2+11^2=13^2$

$36+121 = 169$

157 = 169

Since equality is false, 6,11,13 are not the side lengths of a right triangle.

D

$12^2+16^2=20^2$

$144+256 = 400$

400 = 400

Since equality is true, 12,16,20 could be the side lengths of a right triangle.

Answer: D 12,16,20

Answer 2

Answer:

Choice D

Step-by-step explanation:

If you check each one plugging in your info into this you can get $a^{2} +b^{2} =c^{2}$ that 12² + 16² will equal 400 which is the same as 20².